Problem: Simplify the following expression: $ p = \dfrac{n - 10}{-7} - \dfrac{1}{9} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{n - 10}{-7} \times \dfrac{9}{9} = \dfrac{9n - 90}{-63} $ Multiply the second expression by $\dfrac{-7}{-7}$ $ \dfrac{1}{9} \times \dfrac{-7}{-7} = \dfrac{-7}{-63} $ Therefore $ p = \dfrac{9n - 90}{-63} - \dfrac{-7}{-63} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{9n - 90 + 7 }{-63} $ Distribute the negative sign: $p = \dfrac{9n - 90 + 7}{-63}$ $p = \dfrac{9n - 83}{-63}$ Simplify the expression by dividing the numerator and denominator by -1: $p = \dfrac{-9n + 83}{63}$